"If Europe has solidarity and we have also shown solidarity towards others, then we need to show solidarity now," she said in Berlin. "Everything must move quickly."
Luxembourg said the meeting would focus on policies for sending some migrants home and measures to prevent human trafficking.
Seven people died when their boat sank off Libya's coast, the second such tragedy at sea in days. The Italian coastguard said 1600 migrants had been rescued in the Mediterranean and brought to Italy over the weekend.
At least 2500 migrants have died since January, most of them drowning in the Mediterranean after arduous journeys fleeing war, oppression or poverty in Syria and other parts of the Middle East and Africa or beyond.
The horrors faced by migrants were brought to the heart of the European mainland on Friday when 71 bodies, including a baby girl and three other children, were found in an abandoned refrigeration truck in Austria.
The dead, believed to be refugees from Syria or possibly Afghanistan, had been packed into the truck with just 1sq m of space per five people, police said. Initial tests indicated they had suffocated. Hungarian police arrested a fifth suspect, a Bulgarian citizen, in connection with the deaths. Three Bulgarians and one Afghan had already been arrested.
Three Syrian children taken to hospital with severe dehydration after being rescued in Austria from a van packed with migrants had "vanished" with their parents, said police, who believe they went to Germany.
The two 5-year-old girls and one 6-year-old boy were among 26 migrants in the back of a van pulled over by police near the German border.
Like many migrants caught in Austria - as well as the truck with the 71 bodies - the Fiat Ducato with Spanish number plates, driven by a Romanian, began its journey in Hungary and was headed for Germany.
Britain, France and Germany want the EU to set up migrant reception centres quickly in frontline countries such as Italy and Greece. Their purpose would be to distinguish genuine asylum-seekers fleeing war or persecution from economic migrants who would be sent home.
The three countries want the centres set up "by the end of the year", according to a French official.
The three governments also called for the EU to draw up a list of "safe countries of origin". Applications for asylum by nationals of those countries would automatically be rejected.
The proposals came a day after Theresa May, the British Home Secretary, discussed with her French and German counterparts in Paris the urgent need for reception centres in the countries where migrants first arrive in the EU. A joint statement by the three ministers "underlined the necessity to take immediate action to deal with the challenge from the migrant influx".
The number of migrants reaching the EU's borders has doubled this year, with nearly 340,000 arriving between January and July, compared with 123,500 during the same period in2014.
Most landed in Italy and Greece after crossing the Mediterranean in boats.
"As long as we have not got reception centres in the countries where migrants arrive, and as long as we are not discouraging more people to cross the Mediterranean by sending illegal migrants back, this crisis will just keep escalating," the French official said.
Pope Francis appealed for better international co-operation against people-smugglers in response to the deaths of the 71 migrants found in Austria.
Britain, France and Germany are also urging some EU states to revise their policy on migrants, according to diplomatic sources. Laurent Fabius, the French Foreign Minister, criticised Hungary for building a fence to keep out migrants along its border with Serbia.
Manuel Valls, the French Prime Minister, said people fleeing war and persecution "must be welcomed" in France and treated with dignity.
Merkel, facing her country's biggest refugee crisis since World War II, called on EU counterparts to take on a greater share of the influx of asylum seekers.
"What is happening at the moment is not just," Merkel said. "If Europe is a place of solidarity - and we have also often shown our solidarity - then we must on this question remain solidly united.
"In order to help those who are in distress, we must also be able to tell those who aren't in this situation that they can't remain with us. It's all dependent on being able to make this determination as quickly as possible."
Germany has gone through some soul-searching in the past week after violent protests outside a refugee shelter in the eastern city of Heidenau. About 20 buildings designated as refugee centres have gone up in flames this year in the country.
German media outlets have provided blanket coverage of the crisis. Bild Zeitung, the country's biggest-circulation newspaper, on Saturday devoted the first four pages to a campaign to get average citizens to help. Der Spiegel featured a 12-page cover story that the influential weekly called a "manifesto" for Germans to decide what kind of country they want to live in. "To those who say we can't accept any asylum seekers, I say: 'Yes, we can and we must, and if we do it in a smart way it'll even benefit us,"' German Interior Minister Thomas de Maiziere said in Berlin. "And those who say that all the weary and burdened can come to Germany because we're a rich country, to those I say: 'No, that'snot possible. That overburdens even us."'
Switzerland says it will send financial assistance to help Balkans nations. The Swiss Foreign Ministry on Sunday confirmed a report in the NZZ am Sonntag weekly that the wealthy Alpine nation aimed to send financial aid to Serbia, Macedonia and Bosnia- to help them deal with the ballooning migrant crises on their territories.
EU measures
•Summit: Emergency meeting to discuss solutions on September 14.
•Naval mission: EU rescue efforts in Mediterranean began in June.
•Emergency help: €2.4 billion for countries struggling with surge.
•Relocation: EU states pledging to take in about 32,000 asylum-seekers from Italy and Greece. Permanent relocation system to be agreed on this year.
•Resettlement: Scheme to take in 22,000 Syrian refugees from camps outside Europe to begin soon.
•Hotspots: Other EU states to assist Italy and Greece in identifying and fingerprinting migrants at ports of Catania and Piraeus.
•Deportation: EU compiling list of "safe" states for whose citizens deportation will be almost automatic.
- Graphic News
- additional reporting: Washington Post-Bloomberg, AFP